Deriving forces from an energy potential

Click For Summary
SUMMARY

The discussion focuses on deriving forces from the Keating potential, specifically for silicon and oxygen atoms in a molecular dynamics context. The user, pholvey, seeks to formulate an equation for forces to enhance the efficiency of a conjugate gradient optimization process. Key variables include force constants A, B, and C, the equilibrium Si-O bond length r_0, and the average oxygen bond angle theta_0. The user requests assistance with differentiating a dot product summation to achieve this goal.

PREREQUISITES
  • Understanding of the Keating potential in molecular dynamics.
  • Familiarity with vector calculus, particularly derivatives of dot products.
  • Knowledge of conjugate gradient optimization techniques.
  • Basic concepts of molecular bonding, specifically Si-O interactions.
NEXT STEPS
  • Study the derivation of forces from the Keating potential in molecular simulations.
  • Learn about vector calculus, focusing on derivatives of dot products.
  • Research conjugate gradient optimization methods and their applications in computational chemistry.
  • Explore the mathematical formulation of energy potentials in molecular dynamics.
USEFUL FOR

Researchers in computational chemistry, molecular dynamics practitioners, and anyone involved in optimizing energy calculations for silicon-oxygen systems.

pholvey
Messages
5
Reaction score
0

Homework Statement


This is not a homework problem. I'm trying to do this for research purposes. I have an energy potential (the Keating potential) of the following form (attached). In this form, A, B, and C are force constants, and r_ab is the vector along the bond between atoms a and b. For my purposes, subscripts i and i' represent silicon atoms while j and k represent oxygen atoms. r_0 is the equilibrium Si-O bond length and theta_0 is the average oxygen bond angle.

From this form, I need to derive an equation describing the forces so that I can speed up a conjugate gradient optimization so I don't have to keep estimating the gradient from multiple calls to the energy function.

Homework Equations



r_ij = r_i - r_j (where r's are vectors)

cos theta_ijk = (r_ij dot r_ik)/(abs(r_ij)*abs(r_ik))

The Attempt at a Solution



Honestly, I'm at a loss as to how to even attempt a solution to this problem. Any help/guidance on the subject would be appreciated.

Many thanks,

pholvey
 

Attachments

  • KeatingPotential.jpg
    KeatingPotential.jpg
    10.4 KB · Views: 520
Physics news on Phys.org
Does anyone have any idea on this? Even showing me how to take the derivative of a dot product summation would be greatly appreciated. Thanks.
 

Similar threads

The connection between potential energy and force
  • · Replies 2 ·
Replies
2
Views
1K
What is the relationship between a force field and a potential field?
  • · Replies 2 ·
Replies
2
Views
2K
Is potential energy defined only for internal conservative forces?
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Kinetic Energy and Potential Energy of Electrons
  • · Replies 15 ·
Replies
15
Views
3K
Finding the potential energy of a gravitational force?
  • · Replies 4 ·
Replies
4
Views
2K
Force components for mass attached to two springs
  • · Replies 15 ·
Replies
15
Views
2K
Gradient of a potential energy function
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Chemical Potential from Energy Derivatives
  • · Replies 4 ·
Replies
4
Views
2K
Why is the electric force the negative of the position derivative of EPE?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad What is the zero point for Potential Energy and how to find it from integral limits?
  • · Replies 6 ·
Replies
6
Views
2K